Thank you aghadowey!
Well, the "legend" in the family says that they were from Mountrath, although I have nothing to prove that. The only location reference I've found were references to Queen's County on records. I'm told they were Episcopalian.
I'll try posting the info I have below like you suggested:
Denis & Bridget Moore are the couple I'm seeking. Denis was born roughly 1814 and Bridget (nee Law) around 1821. They were living in Scotland in 1851 and the census gives "Queens County" as where they were from. Also living with them were Denis' brother Anthony Moore (b. ~1831, Queens County) and Denis' nephew Fenton (b. ~1831, Queens County).
So now I know there were at least three Moore boys of Queens County.
On Denis' second marriage record his father is given as Fenton Moore, butcher. So this would place his father's birth pre 1800.
While combing records for my ancestors I've come up with two records that sure seem like they could/should be related but can't link them yet.
One is for a Denis Moore b. ~1817 who deserted the 77th Foot. This Denis was born "Clonena (as they spelled it), Queens County"
The other record was for a Fenton Moore b. ~1807, Mountrath, Clonena, Queens County and belonged ot the 48th of Foot.
So I have all these fragmented pieces. Surely at least some of these men have a record of their birth somewhere. As my family believes they came from Mountrath and records so far offer Queens County as a birthplace, I was hoping both cases were true.
So then I guess I would need to check the Church of Ireland records for Mountrath? Does anyone know if there are any records online? I live in the U.S.
Many thanks for your help!

Brenda